An adaptable generalization of Hotelling’s $T^{2}$ test in high dimension
An adaptable generalization of Hotelling’s $T^{2}$ test in high dimension
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DOI：
10.1214/19-aos1869
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发表时间：
2016-09
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影响因子：
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通讯作者：
Haoran Li;Alexander Aue;D. Paul;Jie Peng;Pei Wang
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文献类型：
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作者：
Haoran Li;Alexander Aue;D. Paul;Jie Peng;Pei Wang
我们提出了一个两个样本的测试，用于检测平均向量之间的差异，在一个高维制度的基础上脊正则化霍特林的$T^2$。为了选择正则化参数，推导出一种方法，其目的是在一类局部替代方案内最大化功率。我们还提出了一个复合测试，结合了最佳的测试，对应于一个特定的收集当地的替代品。建立了对应于岭正则化Hotelling的T^2 $的随机过程的弱收敛性，并用于导出所提出的检验的截止值。对一类亚高斯分布的大样本性质进行了验证。通过广泛的模拟研究，复合材料测试显示出有利的主机对现有的两个样本的测试程序在广泛的设置。所提出的测试程序的性能说明通过应用程序的乳腺癌数据集，其目标是检测不同的DNA拷贝数改变乳腺癌亚型的途径。
We propose a two-sample test for detecting the difference between mean vectors in a high-dimensional regime based on a ridge-regularized Hotelling's $T^2$. To choose the regularization parameter, a method is derived that aims at maximizing power within a class of local alternatives. We also propose a composite test that combines the optimal tests corresponding to a specific collection of local alternatives. Weak convergence of the stochastic process corresponding to the ridge-regularized Hotelling's $T^2$ is established and used to derive the cut-off values of the proposed test. Large sample properties are verified for a class of sub-Gaussian distributions. Through an extensive simulation study, the composite test is shown to compare favorably against a host of existing two-sample test procedure in a wide range of settings. The performance of the proposed test procedure is illustrated through an application to a breast cancer data set where the goal is to detect the pathways with different DNA copy number alterations across breast cancer subtypes.